Vehicle on a Leveled Circular Road

For a vehicle of mass $m$ moving at speed $v$ on a level (unbanked) circular road of radius $r$, three forces act: weight $mg$ (down), normal force $N$ (up), and — critically — the static friction $F_s$ between tyre and road, directed horizontally inward, which alone provides the centripetal force (since the road is level, $N$ simply balances $mg$ and contributes no horizontal component):

Two regimes follow directly:

• Safe turn: if $\dfrac{mv^2}{r}\le\mu_smg$, i.e. $v\le\sqrt{\mu_srg}$, static friction can fully supply the needed centripetal force.
• Skid: if $\dfrac{mv^2}{r}>\mu_smg$, i.e. $v>\sqrt{\mu_srg}$, friction is insufficient, and the vehicle skids outward off its intended circular path. …